Human Height estimation using person detection techniques
Eh, "I won't be using camera calibration." .. Not sure, what you mean.

1st

At first, imagine a sheet of paper laying there on the floor. And first to try to transform the paper sheet (i.e. with some text on it), the picture of the sheet angled by paralaxe to the straight view: Just a transformation by a matrix. It would be highly valuable to have there some floor of square tiles. And once you would estimate/set size of the tiles on the floor, you can then transform the paper sheet.

Then, also some vertical calibration will be needed: Wherever within the scene. A wall of tiles of known shape &amp; size would be perfect. But not really necessary: Any known/premeasured chair would be enough! ..rather two such chairs, in an opposite nooks, for numerical stability.

So yes, that could be treated as "camera calibration". 

2nd

Then you can advance to the next level of the image processing:


Once you see feet of the person, on which tile of the floor the person stays,
and with the known vertical direction,


by the hid/covered known background, you can decide their height, pretty precisely, yes.

The "known background"

Just two images should be enough, of the background place: empty non-occupied, and hid/covered. The clear-empty room can be taken either onence, or periodically, or even just a partial image should be enough: just to detect shape of the person-figure.

3rd

And the third level: Really high. The person could stay in some deformed position. By interpolation of the known human skeleton to the shape of the person-figure on the screen, you can assume the curves of the skeleton of the person, so your estimated/measured total height of the person would be immune to the non-strightened angles in joints of their limbs/backbone. So even if the person knows about your observing, the AI would not get fooled. But you would need/find more refencial points on their body, to interconnect the 2D shape to the internal 3D model.

quantity of snaps in general

More snaps of the person, as they walk through the room, would be helpful: Any model, set up by any single image, should be verifiable/applicable to each of the rest of the images of the same person. Again: stability and "back testing", verifications, robustness.

You are not limited to just a single image, you can have as many as your camera is able to make. So use them, to get not only the measured size, but also to level up the "probability" of the measured result, the accuracy.

On the other hand, you can also flip the coin, and to try to guess the maximum info from the minimum snaps of the scene. But it does not seem, this would be your case. Still: Processing 24 fps recording 20 seconds long.. That definitely requires some power/time to process.

Summary

The 3D models are necessary: Of the surrounding space, of the outer shapes of the person-figure, of the internal structure of the measured body.